Finite Group DatabasebetaFinite Group Databasebeta| order | 3616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#14268647 |
| Fitting | C22×C4×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D113 |
| commutator, cosocle | C2×C113 | C24 |
| Frattini | C2 | C23×D113 |
| Fitting | C22×C4×C113 | C2 |
| socle | C22×C113 | C23 |
| hypercenter | C22×C4 | D113 |
| hypocenter | C113 | C2×#41 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1808 |
916 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3616, 189);